Figures

Figure 1. Modern pollen samples used in this study from the Neotoma Paleoecological Database.

Figure 1. Modern pollen samples used in this study from the Neotoma Paleoecological Database.

Figure 2. The Southwest United States (SWUS) as defined here, showing locations of fossil pollen samples used in this study. Background shading indicates mean July temperature for 1961 - 1990 from PRISM (Daly et al., 2008, 2015; PRISM Climate Group, 2019) at 800-m resolution. The solid gray box outlines the area studied by Bocinsky and Kohler (2014); the green dashed box shows the extent of the reconstruction in this study.

Figure 2. The Southwest United States (SWUS) as defined here, showing locations of fossil pollen samples used in this study. Background shading indicates mean July temperature for 1961 - 1990 from PRISM (Daly et al., 2008, 2015; PRISM Climate Group, 2019) at 800-m resolution. The solid gray box outlines the area studied by Bocinsky and Kohler (2014); the green dashed box shows the extent of the reconstruction in this study.

Figure 3. Temperature for the North Atlantic using Richard Alley’s (2000) Greenland ice core data for 18,000 BC to present with the Younger Dryas and the general period of the northward expansion of maize agriculture from Mesoamerica into the SWUS highlighted.

Figure 3. Temperature for the North Atlantic using Richard Alley’s (2000) Greenland ice core data for 18,000 BC to present with the Younger Dryas and the general period of the northward expansion of maize agriculture from Mesoamerica into the SWUS highlighted.

Figure 4. Low-frequency component of the Moberg et al. (2005) multi-proxy reconstruction for Northern Hemisphere for AD 133–1925. Anomaly is calculated in comparison to the 1961–1990 average.

Figure 4. Low-frequency component of the Moberg et al. (2005) multi-proxy reconstruction for Northern Hemisphere for AD 133–1925. Anomaly is calculated in comparison to the 1961–1990 average.

Figure 5. Low-frequency bootstrapped temperature anomaly loess reconstruction from this study (blue) with standard error (gray). Boxplots show estimates binned by century. Anomalies are calculated in comparison to the 1961–1990 average. The temperature predictions for each sample (not binned by century) are shown by circles; sizes of circles are inversely proportional to the sample-specific errors (size of circle ∝ 1/s1; see Simpson, 2007: 21 for calculation of s1). Anomaly estimates with larger circles are more precise.

Figure 5. Low-frequency bootstrapped temperature anomaly loess reconstruction from this study (blue) with standard error (gray). Boxplots show estimates binned by century. Anomalies are calculated in comparison to the 1961–1990 average. The temperature predictions for each sample (not binned by century) are shown by circles; sizes of circles are inversely proportional to the sample-specific errors (size of circle ∝ 1/s1; see Simpson, 2007: 21 for calculation of s1). Anomaly estimates with larger circles are more precise.

Figure 6. Low-frequency July temperature anomaly for the SWUS from this study, the North American July temperature reconstruction (Viau et al., 2006) from 3000 BC to AD 2000, and the terrestrial composite for 30–60 °N (Kaufman et al., 2020), from 3300 BC to AD 1700, in 500-year bins. All series standardized to a mean of 0 and an s of 1 over the period in this graph.

Figure 6. Low-frequency July temperature anomaly for the SWUS from this study, the North American July temperature reconstruction (Viau et al., 2006) from 3000 BC to AD 2000, and the terrestrial composite for 30–60 °N (Kaufman et al., 2020), from 3300 BC to AD 1700, in 500-year bins. All series standardized to a mean of 0 and an s of 1 over the period in this graph.

Figure 7. Low-frequency July temperature anomaly for the SWUS from this study and the Northern Hemisphere low-frequency component (Moberg et al. 2005) from AD 133 to 1900. Both series have been standardized to a mean of 0 and an s of 1 for this period.

Figure 7. Low-frequency July temperature anomaly for the SWUS from this study and the Northern Hemisphere low-frequency component (Moberg et al. 2005) from AD 133 to 1900. Both series have been standardized to a mean of 0 and an s of 1 for this period.

Tables

Table 1. Metadata for the fossil pollen records (37 sites or 41 datasets) used in this study that have data after 3,550 BC. All data were downloaded from the Neotoma Paleoecological Database (Williams et al., 2018).
Site Name Site ID Dataset ID No. of Samples Elevation (m) Longitude Latitude Pass significance test?
Alpine Pond 9814 14517 26 3200 -112.8245 37.63632 No
Alpine Pond 9814 14547 11 3200 -112.8245 37.63632 No
Bear Lake 10000 14951 12 2778 -112.1472 36.37112 Yes
Bechan Cave 244 3060 12 1280 -110.8667 37.36667 No
Beef Pasture 246 250 90 3060 -108.1604 37.47310 Yes
Beef Pasture 246 25551 71 3060 -108.1604 37.47310 Yes
Cascade Fen [Engineer Mountain Bog] 339 347 63 2690 -107.8087 37.64764 No
Chihuahueños Bog 13680 20833 18 2925 -106.5105 36.04767 No
Columbine Ranch Fen 486 498 28 2694 -107.8157 37.60664 No
Como Lake 2957 3056 9 3523 -105.5142 37.56952 Yes
Crane Lake 504 517 7 2590 -112.1489 36.52986 Yes
Cumbres Bog 11617 17419 30 3100 -106.4505 37.02175 Yes
Fracas Lake 9997 14944 7 2512 -112.2386 36.63070 NA (removed in a previous step)
Hay Lake 982 1013 5 2780 -109.4250 34.00000 Yes
Head Lake 2955 3054 9 2300 -105.7406 37.71109 No
Hermit Lake 23930 41580 26 3450 -105.6317 38.08806 Yes
Hospital Flat Meadow 26738 46801 10 2747 -109.8774 32.66757 No
Hunters Lake 13486 20304 20 3516 -106.8437 37.61104 No
Jacob Lake 1127 1162 5 2285 -110.8333 34.33333 Yes
Lake Emma 10061 15106 8 3740 -107.6154 37.90210 No
Leonora Curtin 14632 22948 12 1850 -106.1065 35.56948 No
Long Lake 1609 1660 2 2727 -108.8333 36.00556 Yes
Lowder Creek Bog 9830 14549 12 3127 -112.7922 37.67214 No
Mayberry Well 1661 1717 1 2080 -108.3000 33.70000 Yes
Molas Lake 1705 1761 25 3200 -107.6827 37.74759 Yes
Molas Pass Bog 1706 1762 15 3220 -107.6975 37.73778 No
Montezuma Well 1710 1766 31 1081 -111.7523 34.64920 No
Posy Lake 1905 1970 14 2653 -111.6960 37.93746 No
Potato Lake 1906 3560 14 2205 -111.3453 34.46222 No
Potato Lake 1906 3561 15 2205 -111.3453 34.46222 Yes
Purple Lake 13683 20838 39 3226 -111.5712 38.07438 Yes
Sagehen Marsh 2241 2320 10 2085 -108.5039 37.47389 Yes
Sagehen Marsh 2241 3608 4 2085 -108.5039 37.47389 No
San Agustin Plains 2260 3612 6 2069 -108.2500 33.86667 Yes
San Luis Lake 9878 14650 24 2293 -105.7247 37.67773 No
Soldier Creek Meadow 24232 42645 16 2860 -109.9204 32.70177 Yes
Stewart Bog 10191 15356 102 3115 -105.7220 35.83200 No
Stoneman Lake 10449 15967 17 2047 -111.5178 34.77887 No
Twin Lakes 2785 2880 54 3290 -108.1026 37.46906 No
Utricularia Lake 2800 2897 11 2753 -108.8083 35.96889 No
Whiskey Lake 2853 2950 12 2712 -108.8108 35.98194 Yes

Supplemental Materials

Supplemental Figures

Supplemental Figure S1. Squared residual length for the fossil assemblages vs age. Red line marks the 95% limit of the calibration set residual lengths (very poorly fitted). We removed all samples that fell above the 95% line.

Supplemental Figure S1. Squared residual length for the fossil assemblages vs age. Red line marks the 95% limit of the calibration set residual lengths (very poorly fitted). We removed all samples that fell above the 95% line.

Supplemental Figure S2. Summary diagram of the results of a MAT model applied to predict temperature from the modern pollen data set. The leave-one-out error measure (RMSEP) shows that 4 analogs provide the optimal choice (lowest RMSEP).

Supplemental Figure S2. Summary diagram of the results of a MAT model applied to predict temperature from the modern pollen data set. The leave-one-out error measure (RMSEP) shows that 4 analogs provide the optimal choice (lowest RMSEP).

Supplemental Figure S3. Time series plot of the minimum dissimilarity between each core (fossil) sample and the modern pollen training set samples. The dotted, horizontal lines are drawn at various percentiles of the distribution of the pair-wise dissimilarities for the training set samples. We used the 5th percentile as the cutoff for good analogs. So, samples with distances greater than the 5th percentile (above the line) were removed.

Supplemental Figure S3. Time series plot of the minimum dissimilarity between each core (fossil) sample and the modern pollen training set samples. The dotted, horizontal lines are drawn at various percentiles of the distribution of the pair-wise dissimilarities for the training set samples. We used the 5th percentile as the cutoff for good analogs. So, samples with distances greater than the 5th percentile (above the line) were removed.

Supplemental Figure S4. Linear regression and scatterplot between temperature anomaly predicted values and the bootstrapped temperature predictions. There is a strong linear relationship across their joint ranges (r2 = 0.96; p > F < .001).

Supplemental Figure S4. Linear regression and scatterplot between temperature anomaly predicted values and the bootstrapped temperature predictions. There is a strong linear relationship across their joint ranges (r2 = 0.96; p > F < .001).

Supplemental Figure S5. Low-frequency weighted bootstrapped temperature anomaly loess reconstruction from this study (blue) with standard error (gray). As in Figure 5 (main text) except here the loess curve (only) is weighted by the inverse of the sample-specific errors s1; see Simpson, 2007: 21 for calculation). Bubble size α 1/s1.

Supplemental Figure S5. Low-frequency weighted bootstrapped temperature anomaly loess reconstruction from this study (blue) with standard error (gray). As in Figure 5 (main text) except here the loess curve (only) is weighted by the inverse of the sample-specific errors s1; see Simpson, 2007: 21 for calculation). Bubble size α 1/s1.

Supplemental Tables

Supplemental Table S1. Results of random TF tests and summaries of MAT prediction output for the fossil pollen cores. Random TF test output is shown for the fossil pollen datasets that were included in the random TF test (36 sites or 40 datasets), which was after some samples were removed using squared residual length. An NA denotes that the site was removed after not passing the significance test.
Site Name Site ID Dataset ID Proportion explained variance Random TF p Anomaly (°C) Anomaly Bootstrapped (°C) Mean boostrap RMSEP (°C) Mean boostrap s1
Bear Lake 10000 14951 0.38 0.02 6.47 5.24 3.67 2.03
Beef Pasture 246 250 0.24 0.04 5.49 5.74 4.13 0.89
Beef Pasture 246 25551 0.29 0.09 4.28 4.16 4.12 1.10
Como Lake 2957 3056 0.42 0.00 6.24 4.50 2.65 0.99
Crane Lake 504 517 0.41 0.03 3.40 2.73 4.47 1.66
Cumbres Bog 11617 17419 0.17 0.06 13.13 11.84 3.79 1.45
Hay Lake 982 1013 0.19 0.02 2.57 2.28 4.47 1.07
Hermit Lake 23930 41580 0.16 0.08 3.81 3.39 4.27 1.15
Jacob Lake 1127 1162 0.35 0.02 2.32 2.81 4.48 0.81
Long Lake 1609 1660 0.13 0.05 7.26 6.61 4.62 1.21
Molas Lake 1705 1761 0.30 0.00 4.74 4.04 4.59 0.69
Potato Lake 1906 3561 0.42 0.00 1.85 1.32 2.76 0.73
Purple Lake 13683 20838 0.55 0.00 2.36 1.54 3.90 0.79
Sagehen Marsh 2241 2320 0.40 0.07 4.20 3.59 3.69 1.02
San Agustin Plains 2260 3612 0.52 0.01 0.00 0.00 3.10 0.95
Soldier Creek Meadow 24232 42645 0.20 0.07 3.75 4.10 4.26 0.72
Whiskey Lake 2853 2950 0.46 0.04 9.81 10.01 2.71 1.61
Alpine Pond 9814 14517 0.03 0.82 NA NA NA NA
Alpine Pond 9814 14547 0.21 0.53 NA NA NA NA
Bechan Cave 244 3060 0.18 0.45 NA NA NA NA
Cascade Fen [Engineer Mountain Bog] 339 347 0.06 0.76 NA NA NA NA
Chihuahueños Bog 13680 20833 0.11 0.42 NA NA NA NA
Columbine Ranch Fen 486 498 0.06 0.72 NA NA NA NA
Head Lake 2955 3054 0.05 0.75 NA NA NA NA
Hospital Flat Meadow 26738 46801 0.30 0.24 NA NA NA NA
Hunters Lake 13486 20304 0.30 0.11 NA NA NA NA
Lake Emma 10061 15106 0.16 0.38 NA NA NA NA
Leonora Curtin 14632 22948 0.27 0.26 NA NA NA NA
Lowder Creek Bog 9830 14549 0.11 0.58 NA NA NA NA
Mayberry Well 1661 1717 0.23 0.07 NA NA NA NA
Molas Pass Bog 1706 1762 0.15 0.57 NA NA NA NA
Montezuma Well 1710 1766 0.06 0.56 NA NA NA NA
Posy Lake 1905 1970 0.03 0.86 NA NA NA NA
Potato Lake 1906 3560 0.43 0.11 NA NA NA NA
Sagehen Marsh 2241 3608 0.53 0.33 NA NA NA NA
San Luis Lake 9878 14650 0.05 0.80 NA NA NA NA
Stewart Bog 10191 15356 0.05 0.47 NA NA NA NA
Stoneman Lake 10449 15967 0.14 0.17 NA NA NA NA
Twin Lakes 2785 2880 0.06 0.67 NA NA NA NA
Utricularia Lake 2800 2897 0.21 0.32 NA NA NA NA
Supplemental Table S2. Final reconstruction output from the loess model for 2999 BC to AD 1996.
Year Temperature Anomaly (°C) Confidence Interval Standard Error
-2999 -1.0329622 1.8654676 0.9478002
-2998 -1.0347158 1.8597342 0.9448872
-2997 -1.0364651 1.8540156 0.9419817
-2996 -1.0382100 1.8483119 0.9390838
-2995 -1.0399506 1.8426232 0.9361935
-2994 -1.0416869 1.8369495 0.9333108
-2993 -1.0434187 1.8312908 0.9304358
-2992 -1.0451462 1.8256473 0.9275684
-2991 -1.0468693 1.8200189 0.9247088
-2990 -1.0485879 1.8144059 0.9218569
-2989 -1.0503022 1.8088081 0.9190128
-2988 -1.0520119 1.8032256 0.9161765
-2987 -1.0537172 1.7976586 0.9133480
-2986 -1.0554181 1.7921071 0.9105274
-2985 -1.0571144 1.7865711 0.9077147
-2984 -1.0588062 1.7810507 0.9049099
-2983 -1.0604935 1.7755459 0.9021131
-2982 -1.0621762 1.7700568 0.8993242
-2981 -1.0638544 1.7645835 0.8965434
-2980 -1.0655280 1.7591261 0.8937705
-2979 -1.0671970 1.7536845 0.8910058
-2978 -1.0688614 1.7482588 0.8882491
-2977 -1.0705211 1.7428491 0.8855006
-2976 -1.0721763 1.7374555 0.8827602
-2975 -1.0738267 1.7320780 0.8800280
-2974 -1.0754725 1.7267166 0.8773041
-2973 -1.0771136 1.7213715 0.8745883
-2972 -1.0787500 1.7160426 0.8718809
-2971 -1.0803817 1.7107301 0.8691817
-2970 -1.0820087 1.7054339 0.8664908
-2969 -1.0836309 1.7001542 0.8638083
-2968 -1.0852483 1.6948910 0.8611342
-2967 -1.0868610 1.6896443 0.8584685
-2966 -1.0884688 1.6844142 0.8558112
-2965 -1.0900719 1.6792008 0.8531624
-2964 -1.0916701 1.6740042 0.8505221
-2963 -1.0932634 1.6688242 0.8478903
-2962 -1.0948519 1.6636611 0.8452671
-2961 -1.0964356 1.6585149 0.8426524
-2960 -1.0980143 1.6533857 0.8400463
-2959 -1.0995881 1.6482734 0.8374489
-2958 -1.1011570 1.6431781 0.8348601
-2957 -1.1027210 1.6380999 0.8322800
-2956 -1.1042800 1.6330389 0.8297086
-2955 -1.1058340 1.6279951 0.8271460
-2954 -1.1073831 1.6229685 0.8245921
-2953 -1.1089271 1.6179593 0.8220470
-2952 -1.1104661 1.6129674 0.8195107
-2951 -1.1120001 1.6079929 0.8169833
-2950 -1.1135291 1.6030358 0.8144648
-2949 -1.1150529 1.5980963 0.8119551
-2948 -1.1165717 1.5931743 0.8094543
-2947 -1.1180854 1.5882699 0.8069625
-2946 -1.1195940 1.5833832 0.8044797
-2945 -1.1210974 1.5785142 0.8020059
-2944 -1.1225958 1.5736629 0.7995411
-2943 -1.1240889 1.5688295 0.7970853
-2942 -1.1255769 1.5640139 0.7946386
-2941 -1.1270596 1.5592162 0.7922010
-2940 -1.1285372 1.5544364 0.7897726
-2939 -1.1300095 1.5496747 0.7873532
-2938 -1.1314767 1.5449310 0.7849431
-2937 -1.1329385 1.5402054 0.7825421
-2936 -1.1343951 1.5354979 0.7801503
-2935 -1.1358464 1.5308086 0.7777678
-2934 -1.1372924 1.5261375 0.7753946
-2933 -1.1387330 1.5214848 0.7730306
-2932 -1.1401684 1.5168503 0.7706759
-2931 -1.1415983 1.5122342 0.7683306
-2930 -1.1430230 1.5076365 0.7659946
-2929 -1.1444422 1.5030572 0.7636680
-2928 -1.1458560 1.4984965 0.7613508
-2927 -1.1472645 1.4939543 0.7590430
-2926 -1.1486675 1.4894306 0.7567446
-2925 -1.1500650 1.4849256 0.7544557
-2924 -1.1514571 1.4804392 0.7521763
-2923 -1.1528437 1.4759715 0.7499064
-2922 -1.1542248 1.4715226 0.7476460
-2921 -1.1556005 1.4670925 0.7453951
-2920 -1.1569706 1.4626811 0.7431539
-2919 -1.1583351 1.4582886 0.7409221
-2918 -1.1596941 1.4539151 0.7387000
-2917 -1.1610475 1.4495604 0.7364875
-2916 -1.1623954 1.4452247 0.7342847
-2915 -1.1637376 1.4409080 0.7320914
-2914 -1.1650742 1.4366103 0.7299079
-2913 -1.1664052 1.4323318 0.7277341
-2912 -1.1677306 1.4280723 0.7255699
-2911 -1.1690502 1.4238320 0.7234155
-2910 -1.1703642 1.4196108 0.7212708
-2909 -1.1716725 1.4154088 0.7191359
-2908 -1.1729751 1.4112261 0.7170108
-2907 -1.1742720 1.4070626 0.7148954
-2906 -1.1755631 1.4029185 0.7127899
-2905 -1.1768484 1.3987937 0.7106941
-2904 -1.1781280 1.3946882 0.7086082
-2903 -1.1794018 1.3906021 0.7065322
-2902 -1.1806697 1.3865354 0.7044660
-2901 -1.1819319 1.3824882 0.7024097
-2900 -1.1831882 1.3784604 0.7003633
-2899 -1.1844387 1.3744521 0.6983268
-2898 -1.1856832 1.3704634 0.6963002
-2897 -1.1869219 1.3664942 0.6942835
-2896 -1.1881547 1.3625445 0.6922768
-2895 -1.1893816 1.3586144 0.6902800
-2894 -1.1906026 1.3547040 0.6882932
-2893 -1.1918176 1.3508131 0.6863163
-2892 -1.1930266 1.3469419 0.6843495
-2891 -1.1942297 1.3430904 0.6823926
-2890 -1.1954267 1.3392586 0.6804458
-2889 -1.1966178 1.3354465 0.6785089
-2888 -1.1978028 1.3316541 0.6765821
-2887 -1.1989817 1.3278814 0.6746653
-2886 -1.2001547 1.3241285 0.6727585
-2885 -1.2013215 1.3203953 0.6708618
-2884 -1.2024822 1.3166820 0.6689751
-2883 -1.2036369 1.3129884 0.6670985
-2882 -1.2047854 1.3093147 0.6652320
-2881 -1.2059278 1.3056607 0.6633755
-2880 -1.2070640 1.3020266 0.6615291
-2879 -1.2081940 1.2984124 0.6596928
-2878 -1.2093179 1.2948180 0.6578665
-2877 -1.2104356 1.2912434 0.6560504
-2876 -1.2115470 1.2876887 0.6542443
-2875 -1.2126522 1.2841539 0.6524484
-2874 -1.2137512 1.2806389 0.6506625
-2873 -1.2148439 1.2771439 0.6488867
-2872 -1.2159303 1.2736687 0.6471211
-2871 -1.2170105 1.2702134 0.6453655
-2870 -1.2180843 1.2667779 0.6436201
-2869 -1.2191518 1.2633624 0.6418847
-2868 -1.2202129 1.2599667 0.6401594
-2867 -1.2212677 1.2565910 0.6384443
-2866 -1.2223161 1.2532351 0.6367393
-2865 -1.2233581 1.2498991 0.6350443
-2864 -1.2243937 1.2465830 0.6333595
-2863 -1.2254229 1.2432867 0.6316847
-2862 -1.2264457 1.2400103 0.6300200
-2861 -1.2274620 1.2367538 0.6283655
-2860 -1.2284718 1.2335171 0.6267210
-2859 -1.2294751 1.2303002 0.6250866
-2858 -1.2304720 1.2271032 0.6234622
-2857 -1.2314623 1.2239260 0.6218480
-2856 -1.2324461 1.2207686 0.6202438
-2855 -1.2334233 1.2176310 0.6186496
-2854 -1.2343940 1.2145131 0.6170655
-2853 -1.2353581 1.2114151 0.6154915
-2852 -1.2363156 1.2083368 0.6139275
-2851 -1.2372665 1.2052782 0.6123735
-2850 -1.2382108 1.2022393 0.6108295
-2849 -1.2391484 1.1992201 0.6092955
-2848 -1.2400794 1.1962206 0.6077716
-2847 -1.2410036 1.1932408 0.6062576
-2846 -1.2419212 1.1902806 0.6047536
-2845 -1.2428321 1.1873400 0.6032595
-2844 -1.2437363 1.1844190 0.6017754
-2843 -1.2446337 1.1815176 0.6003013
-2842 -1.2455244 1.1786356 0.5988370
-2841 -1.2464091 1.1757732 0.5973827
-2840 -1.2472889 1.1729302 0.5959382
-2839 -1.2481638 1.1701066 0.5945036
-2838 -1.2490339 1.1673024 0.5930789
-2837 -1.2498991 1.1645176 0.5916640
-2836 -1.2507595 1.1617522 0.5902589
-2835 -1.2516150 1.1590061 0.5888637
-2834 -1.2524657 1.1562795 0.5874784
-2833 -1.2533114 1.1535721 0.5861029
-2832 -1.2541523 1.1508842 0.5847372
-2831 -1.2549883 1.1482155 0.5833813
-2830 -1.2558193 1.1455662 0.5820352
-2829 -1.2566455 1.1429363 0.5806990
-2828 -1.2574667 1.1403256 0.5793726
-2827 -1.2582831 1.1377342 0.5780560
-2826 -1.2590945 1.1351621 0.5767491
-2825 -1.2599010 1.1326092 0.5754521
-2824 -1.2607025 1.1300756 0.5741648
-2823 -1.2614991 1.1275613 0.5728874
-2822 -1.2622908 1.1250662 0.5716196
-2821 -1.2630775 1.1225903 0.5703617
-2820 -1.2638592 1.1201336 0.5691135
-2819 -1.2646360 1.1176961 0.5678751
-2818 -1.2654078 1.1152777 0.5666463
-2817 -1.2661746 1.1128785 0.5654274
-2816 -1.2669364 1.1104984 0.5642181
-2815 -1.2676933 1.1081375 0.5630186
-2814 -1.2684451 1.1057956 0.5618287
-2813 -1.2691920 1.1034729 0.5606486
-2812 -1.2699338 1.1011692 0.5594781
-2811 -1.2706707 1.0988845 0.5583174
-2810 -1.2714025 1.0966189 0.5571662
-2809 -1.2721292 1.0943723 0.5560248
-2808 -1.2728510 1.0921446 0.5548930
-2807 -1.2735677 1.0899360 0.5537708
-2806 -1.2742793 1.0877462 0.5526583
-2805 -1.2749859 1.0855754 0.5515553
-2804 -1.2756875 1.0834235 0.5504620
-2803 -1.2763840 1.0812905 0.5493783
-2802 -1.2770754 1.0791763 0.5483041
-2801 -1.2777617 1.0770810 0.5472395
-2800 -1.2784430 1.0750044 0.5461845
-2799 -1.2791192 1.0729467 0.5451389
-2798 -1.2797903 1.0709077 0.5441030
-2797 -1.2804562 1.0688874 0.5430765
-2796 -1.2811171 1.0668858 0.5420596
-2795 -1.2817729 1.0649029 0.5410521
-2794 -1.2824235 1.0629386 0.5400541
-2793 -1.2830690 1.0609930 0.5390655
-2792 -1.2837094 1.0590659 0.5380865
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1660 -0.7709029 0.9820758 0.4989696
1661 -0.7699124 0.9840970 0.4999965
1662 -0.7689085 0.9861789 0.5010543
1663 -0.7678923 0.9883115 0.5021378
1664 -0.7668651 0.9904845 0.5032419
1665 -0.7658279 0.9926874 0.5043611
1666 -0.7647820 0.9949097 0.5054902
1667 -0.7637286 0.9971405 0.5066236
1668 -0.7626687 0.9993690 0.5077558
1669 -0.7616037 1.0015841 0.5088813
1670 -0.7605346 1.0037750 0.5099944
1671 -0.7594627 1.0059304 0.5110896
1672 -0.7583890 1.0080394 0.5121611
1673 -0.7573149 1.0100910 0.5132034
1674 -0.7562414 1.0120739 0.5142109
1675 -0.7551697 1.0139774 0.5151780
1676 -0.7541011 1.0157904 0.5160992
1677 -0.7530366 1.0175022 0.5169689
1678 -0.7519774 1.0191021 0.5177818
1679 -0.7509248 1.0205795 0.5185324
1680 -0.7498799 1.0219240 0.5192155
1681 -0.7488438 1.0231254 0.5198259
1682 -0.7478178 1.0241736 0.5203585
1683 -0.7468030 1.0250589 0.5208083
1684 -0.7458006 1.0257715 0.5211703
1685 -0.7448117 1.0263021 0.5214399
1686 -0.7438376 1.0266417 0.5216125
1687 -0.7428794 1.0267814 0.5216835
1688 -0.7419383 1.0267128 0.5216486
1689 -0.7410003 1.0264288 0.5215043
1690 -0.7397307 1.0259533 0.5212627
1691 -0.7380098 1.0253204 0.5209412
1692 -0.7358620 1.0245604 0.5205550
1693 -0.7333117 1.0237060 0.5201209
1694 -0.7303833 1.0227915 0.5196563
1695 -0.7271012 1.0218522 0.5191790
1696 -0.7234899 1.0209231 0.5187070
1697 -0.7195736 1.0200389 0.5182577
1698 -0.7153769 1.0192329 0.5178483
1699 -0.7109241 1.0185369 0.5174946
1700 -0.7062397 1.0179798 0.5172116
1701 -0.7013480 1.0175882 0.5170126
1702 -0.6962735 1.0173848 0.5169093
1703 -0.6910406 1.0173889 0.5169113
1704 -0.6856736 1.0176153 0.5170264
1705 -0.6801970 1.0180748 0.5172598
1706 -0.6746352 1.0187732 0.5176147
1707 -0.6690126 1.0197115 0.5180914
1708 -0.6633535 1.0208859 0.5186881
1709 -0.6576825 1.0222876 0.5194003
1710 -0.6520239 1.0239027 0.5202209
1711 -0.6464021 1.0257129 0.5211406
1712 -0.6408416 1.0276947 0.5221475
1713 -0.6353666 1.0298207 0.5232277
1714 -0.6300017 1.0320591 0.5243649
1715 -0.6247713 1.0343742 0.5255412
1716 -0.6196997 1.0367273 0.5267367
1717 -0.6148114 1.0390761 0.5279301
1718 -0.6101307 1.0413761 0.5290987
1719 -0.6056821 1.0435805 0.5302187
1720 -0.6014900 1.0456410 0.5312656
1721 -0.5975788 1.0475081 0.5322142
1722 -0.5939728 1.0491316 0.5330391
1723 -0.5906966 1.0504613 0.5337147
1724 -0.5877744 1.0514476 0.5342158
1725 -0.5852308 1.0520418 0.5345177
1726 -0.5830913 1.0521999 0.5345980
1727 -0.5814036 1.0519718 0.5344821
1728 -0.5801702 1.0514103 0.5341968
1729 -0.5793738 1.0505401 0.5337547
1730 -0.5789974 1.0493873 0.5331690
1731 -0.5790236 1.0479788 0.5324534
1732 -0.5794352 1.0463425 0.5316220
1733 -0.5802151 1.0445068 0.5306893
1734 -0.5813459 1.0425007 0.5296701
1735 -0.5828105 1.0403536 0.5285792
1736 -0.5845917 1.0380951 0.5274317
1737 -0.5866722 1.0357545 0.5262425
1738 -0.5890349 1.0333615 0.5250266
1739 -0.5916624 1.0309449 0.5237989
1740 -0.5945376 1.0285336 0.5225737
1741 -0.5976433 1.0261555 0.5213654
1742 -0.6009622 1.0238377 0.5201878
1743 -0.6044772 1.0216065 0.5190542
1744 -0.6081710 1.0194871 0.5179774
1745 -0.6120263 1.0175032 0.5169694
1746 -0.6160261 1.0156772 0.5160417
1747 -0.6201530 1.0140298 0.5152047
1748 -0.6243898 1.0125800 0.5144681
1749 -0.6287193 1.0113450 0.5138406
1750 -0.6331244 1.0103399 0.5133299
1751 -0.6375877 1.0095776 0.5129426
1752 -0.6420922 1.0090689 0.5126841
1753 -0.6466204 1.0088222 0.5125588
1754 -0.6511553 1.0088436 0.5125697
1755 -0.6556796 1.0091367 0.5127186
1756 -0.6601761 1.0097028 0.5130062
1757 -0.6646275 1.0105404 0.5134318
1758 -0.6690168 1.0116460 0.5139935
1759 -0.6733265 1.0130133 0.5146882
1760 -0.6775396 1.0146338 0.5155115
1761 -0.6816388 1.0164966 0.5164580
1762 -0.6856068 1.0185888 0.5175210
1763 -0.6894266 1.0208950 0.5186927
1764 -0.6930807 1.0233981 0.5199645
1765 -0.6965521 1.0260790 0.5213266
1766 -0.6998235 1.0289168 0.5227684
1767 -0.7028778 1.0318889 0.5242785
1768 -0.7056975 1.0349715 0.5258447
1769 -0.7082657 1.0381393 0.5274541
1770 -0.7105649 1.0413657 0.5290934
1771 -0.7125781 1.0446235 0.5307486
1772 -0.7142880 1.0478842 0.5324053
1773 -0.7156774 1.0511190 0.5340488
1774 -0.7167290 1.0542982 0.5356641
1775 -0.7174257 1.0573920 0.5372360
1776 -0.7177503 1.0603703 0.5387492
1777 -0.7176854 1.0632028 0.5401883
1778 -0.7172139 1.0658595 0.5415381
1779 -0.7163186 1.0683105 0.5427834
1780 -0.7149822 1.0705260 0.5439091
1781 -0.7131876 1.0724772 0.5449004
1782 -0.7109175 1.0741357 0.5457430
1783 -0.7081547 1.0754737 0.5464229
1784 -0.7048987 1.0764655 0.5469268
1785 -0.7018675 1.0771328 0.5472658
1786 -0.6994194 1.0775241 0.5474646
1787 -0.6975112 1.0776803 0.5475440
1788 -0.6960995 1.0776444 0.5475258
1789 -0.6951411 1.0774613 0.5474327
1790 -0.6945927 1.0771758 0.5472877
1791 -0.6944110 1.0768327 0.5471133
1792 -0.6945528 1.0764753 0.5469318
1793 -0.6949747 1.0761448 0.5467638
1794 -0.6956335 1.0758797 0.5466292
1795 -0.6964858 1.0757150 0.5465455
1796 -0.6974885 1.0756815 0.5465285
1797 -0.6985982 1.0758055 0.5465915
1798 -0.6997716 1.0761082 0.5467452
1799 -0.7009655 1.0766053 0.5469978
1800 -0.7021366 1.0773068 0.5473542
1801 -0.7032415 1.0782169 0.5478166
1802 -0.7042371 1.0793335 0.5483840
1803 -0.7050799 1.0806488 0.5490522
1804 -0.7057269 1.0821489 0.5498144
1805 -0.7061346 1.0838141 0.5506604
1806 -0.7062597 1.0856192 0.5515776
1807 -0.7060591 1.0875340 0.5525504
1808 -0.7054894 1.0895234 0.5535612
1809 -0.7045073 1.0915480 0.5545899
1810 -0.7030695 1.0935650 0.5556146
1811 -0.7011329 1.0955282 0.5566121
1812 -0.6986540 1.0973891 0.5575576
1813 -0.6955896 1.0990975 0.5584256
1814 -0.6918964 1.1006021 0.5591900
1815 -0.6875312 1.1018515 0.5598248
1816 -0.6824506 1.1027950 0.5603042
1817 -0.6766114 1.1033832 0.5606030
1818 -0.6699749 1.1035706 0.5606982
1819 -0.6627891 1.1034012 0.5606122
1820 -0.6552223 1.1029268 0.5603711
1821 -0.6472842 1.1021623 0.5599827
1822 -0.6389843 1.1011234 0.5594549
1823 -0.6303319 1.0998261 0.5587957
1824 -0.6213367 1.0982872 0.5580139
1825 -0.6120082 1.0965236 0.5571178
1826 -0.6023558 1.0945528 0.5561165
1827 -0.5923892 1.0923920 0.5550187
1828 -0.5821178 1.0900590 0.5538333
1829 -0.5715510 1.0875711 0.5525693
1830 -0.5606985 1.0849456 0.5512353
1831 -0.5495698 1.0821999 0.5498403
1832 -0.5381743 1.0793506 0.5483926
1833 -0.5265216 1.0764141 0.5469007
1834 -0.5146212 1.0734065 0.5453726
1835 -0.5024826 1.0703432 0.5438162
1836 -0.4901152 1.0672388 0.5422389
1837 -0.4775288 1.0641075 0.5406480
1838 -0.4647326 1.0609625 0.5390501
1839 -0.4517363 1.0578161 0.5374515
1840 -0.4385494 1.0546800 0.5358581
1841 -0.4251814 1.0515646 0.5342752
1842 -0.4116417 1.0484795 0.5327078
1843 -0.3979400 1.0454330 0.5311599
1844 -0.3840857 1.0424325 0.5296354
1845 -0.3700883 1.0394840 0.5281374
1846 -0.3559574 1.0365927 0.5266683
1847 -0.3417024 1.0337622 0.5252302
1848 -0.3273329 1.0309951 0.5238243
1849 -0.3128584 1.0282928 0.5224513
1850 -0.2982883 1.0256553 0.5211113
1851 -0.2836324 1.0230815 0.5198037
1852 -0.2688999 1.0205693 0.5185272
1853 -0.2541005 1.0181151 0.5172803
1854 -0.2392436 1.0157144 0.5160606
1855 -0.2243388 1.0133616 0.5148652
1856 -0.2093955 1.0110499 0.5136907
1857 -0.1944234 1.0087719 0.5125332
1858 -0.1794319 1.0065189 0.5113886
1859 -0.1644305 1.0042818 0.5102519
1860 -0.1494287 1.0020505 0.5091183
1861 -0.1344361 0.9998143 0.5079821
1862 -0.1194621 0.9975622 0.5068379
1863 -0.1045164 0.9952826 0.5056796
1864 -0.0896083 0.9929636 0.5045014
1865 -0.0747474 0.9905934 0.5032972
1866 -0.0599432 0.9881598 0.5020607
1867 -0.0452052 0.9856511 0.5007861
1868 -0.0305430 0.9830555 0.4994674
1869 -0.0159661 0.9803621 0.4980989
1870 -0.0014839 0.9775601 0.4966753
1871 0.0128940 0.9746398 0.4951916
1872 0.0271581 0.9715926 0.4936433
1873 0.0412989 0.9684106 0.4920266
1874 0.0553083 0.9650883 0.4903387
1875 0.0693531 0.9616946 0.4886144
1876 0.0835512 0.9582807 0.4868799
1877 0.0979004 0.9548488 0.4851362
1878 0.1123987 0.9514010 0.4833844
1879 0.1270438 0.9479397 0.4816259
1880 0.1418337 0.9444674 0.4798617
1881 0.1567662 0.9409866 0.4780931
1882 0.1718391 0.9374999 0.4763216
1883 0.1870504 0.9340099 0.4745484
1884 0.2023979 0.9305195 0.4727751
1885 0.2178795 0.9270315 0.4710029
1886 0.2334930 0.9235489 0.4692334
1887 0.2492363 0.9200745 0.4674682
1888 0.2651072 0.9166116 0.4657088
1889 0.2811037 0.9131633 0.4639568
1890 0.2972235 0.9097327 0.4622138
1891 0.3134647 0.9063233 0.4604815
1892 0.3298249 0.9029384 0.4587618
1893 0.3463021 0.8995816 0.4570562
1894 0.3628941 0.8962564 0.4553668
1895 0.3795989 0.8929666 0.4536953
1896 0.3964142 0.8897160 0.4520437
1897 0.4133380 0.8865085 0.4504141
1898 0.4303680 0.8833481 0.4488084
1899 0.4475023 0.8802392 0.4472288
1900 0.4647385 0.8771860 0.4456775
1901 0.4820747 0.8741930 0.4441569
1902 0.4995086 0.8712651 0.4426693
1903 0.5170382 0.8684069 0.4412171
1904 0.5346612 0.8656237 0.4398030
1905 0.5523756 0.8629207 0.4384297
1906 0.5701792 0.8603035 0.4370999
1907 0.5880698 0.8577777 0.4358167
1908 0.6060455 0.8553495 0.4345830
1909 0.6241039 0.8530252 0.4334020
1910 0.6422430 0.8508114 0.4322772
1911 0.6604607 0.8487149 0.4312121
1912 0.6787547 0.8467431 0.4302103
1913 0.6971230 0.8449036 0.4292756
1914 0.7155635 0.8432043 0.4284123
1915 0.7340739 0.8416536 0.4276244
1916 0.7526522 0.8402603 0.4269165
1917 0.7712962 0.8390334 0.4262931
1918 0.7900038 0.8379827 0.4257593
1919 0.8087729 0.8371181 0.4253200
1920 0.8276014 0.8364502 0.4249807
1921 0.8465299 0.8360263 0.4247653
1922 0.8655888 0.8358819 0.4246919
1923 0.8847749 0.8360219 0.4247631
1924 0.9040847 0.8364517 0.4249814
1925 0.9235146 0.8371764 0.4253496
1926 0.9430612 0.8382015 0.4258705
1927 0.9627211 0.8395326 0.4265467
1928 0.9824909 0.8411750 0.4273812
1929 1.0023669 0.8431345 0.4283768
1930 1.0223459 0.8454166 0.4295363
1931 1.0424244 0.8480272 0.4308627
1932 1.0625988 0.8509721 0.4323589
1933 1.0828657 0.8542570 0.4340279
1934 1.1032217 0.8578880 0.4358727
1935 1.1236634 0.8618711 0.4378964
1936 1.1441872 0.8662125 0.4401022
1937 1.1647897 0.8709186 0.4424932
1938 1.1854674 0.8759958 0.4450729
1939 1.2062198 0.8814550 0.4478465
1940 1.2270482 0.8873060 0.4508193
1941 1.2479532 0.8935551 0.4539943
1942 1.2689351 0.9002077 0.4573743
1943 1.2899943 0.9072691 0.4609621
1944 1.3111313 0.9147437 0.4647597
1945 1.3323465 0.9226357 0.4687695
1946 1.3536402 0.9309487 0.4729931
1947 1.3750129 0.9396856 0.4774321
1948 1.3964650 0.9488490 0.4820878
1949 1.4179969 0.9584408 0.4869612
1950 1.4396089 0.9684627 0.4920531
1951 1.4613016 0.9789157 0.4973640
1952 1.4830753 0.9898003 0.5028942
1953 1.5049304 1.0011167 0.5086438
1954 1.5268673 1.0128646 0.5146127
1955 1.5488865 1.0250434 0.5208004
1956 1.5709883 1.0376519 0.5272065
1957 1.5931731 1.0506889 0.5338303
1958 1.6154414 1.0641525 0.5406708
1959 1.6377935 1.0780407 0.5477271
1960 1.6602300 1.0923513 0.5549980
1961 1.6827510 1.1070815 0.5624821
1962 1.7053572 1.1222287 0.5701780
1963 1.7280489 1.1377898 0.5780842
1964 1.7508265 1.1537615 0.5861991
1965 1.7736903 1.1701406 0.5945209
1966 1.7966409 1.1869234 0.6030479
1967 1.8196786 1.2041064 0.6117781
1968 1.8428038 1.2216858 0.6207098
1969 1.8660170 1.2396577 0.6298409
1970 1.8893185 1.2580183 0.6391695
1971 1.9127088 1.2767635 0.6486935
1972 1.9361882 1.2958893 0.6584109
1973 1.9597571 1.3153917 0.6683196
1974 1.9834161 1.3352667 0.6784176
1975 2.0071654 1.3555100 0.6887027
1976 2.0310055 1.3761178 0.6991730
1977 2.0549368 1.3970858 0.7098264
1978 2.0789597 1.4184101 0.7206608
1979 2.1030746 1.4400866 0.7316741
1980 2.1272819 1.4621113 0.7428643
1981 2.1515820 1.4844803 0.7542295
1982 2.1759754 1.5071897 0.7657676
1983 2.2004624 1.5302356 0.7774767
1984 2.2250435 1.5536142 0.7893548
1985 2.2497190 1.5773217 0.8014000
1986 2.2744893 1.6013544 0.8136105
1987 2.2993549 1.6257088 0.8259844
1988 2.3243162 1.6503811 0.8385198
1989 2.3493736 1.6753679 0.8512150
1990 2.3745275 1.7006657 0.8640682
1991 2.3997782 1.7262711 0.8770777
1992 2.4251263 1.7521808 0.8902418
1993 2.4505720 1.7783915 0.9035589
1994 2.4761159 1.8049000 0.9170272
1995 2.5017583 1.8317031 0.9306452
1996 2.5274997 1.8587978 0.9444114